I visited the museum a few days ago; they are currently in preparation for a special exhibition, so not all of their "star" works are on show. This was disappointing as the entrance fee is a bit high (15 Euro) for what you get at present, which is basically a handful of rooms with a mix of art and furnishings. The decorated rooms on show are absolutely lovely and there are some amazing works of art (I particularly liked the two Corots on show). I understand Helsinki is an expensive city, but I just felt like the price/value ratio maybe wasn't there. If you want to see art in Helsinki that isn't modern or contemporary, my suggestion would be to visit the Ateneum and skip this. It is very nice to see the art hung in a residence as it was intended to be seen, but honestly there are only a few rooms where this is the case.
It's a decent hike from the Esplanade area, but it is on the way to the coast on the southwest side of the city, which is lovely to visit as well.